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Reidemeister torsion on character varieties

Abstract : In this PhD dissertation, we study a topological invariant of 3-manifolds, namely the Reidemeister torsion, as globally defined on character varieties of the fundamental group in SL(2,C). The « adjoint » torsion will be the torsion of the cohomological complex associated to the adjoint representation. We explain that it can be seen as a meromorphic differential form on the character variety, and we aim to understand its poles and zeros. They will be related with -singular points of the character variety -the topology of incompressible surfaces embedded in the 3-manifold, provided by the Culler-Shalen theory. As an application, we prove a relation between the genus of those incompressible surface and the genus of the character variety. The « acyclic » torsion of the standard complex is a rational function on the character variety. We study its poles at infinity in the character variety, and we give sufficient conditions for this torsion to be non constant.
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Submitted on : Wednesday, April 24, 2019 - 2:31:26 PM
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  • HAL Id : tel-02108892, version 1


Léo Bénard. Reidemeister torsion on character varieties. Algebraic Topology [math.AT]. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS020⟩. ⟨tel-02108892⟩



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